"Neither can Live"

[Danger Mouse]

No: HPFGUIDX 73313

So confused... I was re-reading various bits of OoP just now, and spent a few minutes staring at the prophecy... 

Here it is again for those without books:
`The one with the power to vanquish the Dark Lord approaches. born to those who have thrice defied him, born as the seventh month dies . and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not . and either must die at the hand of the other for neither can live while the other survives . the one with the power to vanquish the Dark Lord will be born as the seventh month dies .'

What came to mind was the "neither can live while the other survives" bit... Ermmm... aren't they both living while the other survives? If it was "neither can die," then okey-dokey, I'd get that. It'd be saying that they'd both have to die for the world to be rid of Voldemort... but... it doesn't. So what is this phrase saying?

-Dan

[Non-text portions of this message have been removed]